Problem: Simplify the following expression: $x = \dfrac{k^2 - k - 42}{k - 7} $
Answer: First factor the polynomial in the numerator. $ k^2 - k - 42 = (k - 7)(k + 6) $ So we can rewrite the expression as: $x = \dfrac{(k - 7)(k + 6)}{k - 7} $ We can divide the numerator and denominator by $(k - 7)$ on condition that $k \neq 7$ Therefore $x = k + 6; k \neq 7$